Methane has been measured in the Martian atmosphere at concentrations of approx. 10 ppb. Since the photochemical lifetime of this gas is approx. 300 years, it is likely that methane is currently being released from the surface. Possible sources for the methane include 1) hydrothermal activity, 2) serpentinization of basalts and other water-rock interactions, 3) thermal maturation of sedimentary organic matter, and 4) metabolism of living bacteria. Any such discovery would revolutionize our understanding of Mars. Longitudinal variations in methane concentration, as measured by the Planetary Fourier Spectrometer (PFS) on Mars Express, show the highest values over Arabia Terra, Elysium Planum, and Arcadia-Memnonia, suggesting localized areas of methane release. We are using orbital data and methodologies derived from petroleum exploration in an attempt to locate these release points.